High communication delay is an obstacle of the application of ALM (Application Layer Multicast) technology. Traditional MST problem trying to get a tree with a small tree weight is not fit for ALM. ALM requires the multicast tree has minimum tree diameter, which determines the communicate period of real-time application systems such as DVE and video conferencing system. Based on this point an amended algorithm of Prim algorithm named MDT is presented in this paper. It tries to find a spanning tree for a certain number of nodes with a shortest tree diameter. The algorithm process is discussed in detail and the fake codes are also given out in this paper. A series of simulation experiments had been taken to check the rightness of this algorithm. Algorithm analysis and simulation results have proved that MDT algorithm gets its initial object. Some disadvantages of MDT algorithm are also discussed in the conclusions section.